Connection between quantum-many-body scars and the Affleck–Kennedy–Lieb–Tasaki model from the viewpoint of embedded Hamiltonians

Shiraishi, Naoto

doi:10.1088/1742-5468/ab342e

Cited by 85 publications

(56 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this appendix we explain the relation between the dipole-conserving Hamiltonian H 3 introduced in Eq. (1) and the PXP model [73], that appears in the context of quantum many-body scars [41][42][43]103]. Such relation has been already obtained in Ref.…”

Section: Appendix C: Entanglement Growth From Random Product Statesmentioning

confidence: 60%

Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians

et al. 2020

View full text Add to dashboard Cite

We show that the combination of charge and dipole conservation-characteristic of fracton systems-leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization. As a concrete example, we investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total S z ) and its associated dipole moment. First, we consider a minimal model including only three-site terms and find that the infinite temperature auto-correlation saturates to a finite value-showcasing non-thermal behavior. The absence of thermalization is identified as a consequence of the strong fragmentation of the Hilbert space into exponentially many invariant subspaces in the local S z basis, arising from the interplay of dipole conservation and local interactions. Second, we extend the model by including four-site terms and find that this perturbation leads to a weak fragmentation: the system still has exponentially many invariant subspaces, but they are no longer sufficient to avoid thermalization for typical initial states. More generally, for any finite range of interactions, the system still exhibits non-thermal eigenstates appearing throughout the entire spectrum. We compare our results to charge and dipole moment conserving random unitary circuit models for which we reach identical conclusions.arXiv:1904.04266v2 [cond-mat.str-el]

show abstract

Section: Appendix C: Entanglement Growth From Random Product Statesmentioning

confidence: 60%

Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians

et al. 2020

View full text Add to dashboard Cite

show abstract

“…V below, can be expressed in this "projector embedded" form such that a single target state is embedded -namely the AKLT ground state at zero energy. 59 However, the complete set of N + 1 scarred eigenstates with enhanced support on |Z 2 state (mentioned in Sec. II) have not been understood through this embedding procedure.…”

Section: A Projector Embeddingmentioning

confidence: 99%

Quantum scars as embeddings of weakly broken Lie algebra representations

2020

View full text Add to dashboard Cite

We present an interpretation of scar states and quantum revivals as weakly "broken" representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system. We show that the PXP model, describing strongly-interacting Rydberg atoms, supports a "loose" embedding of multiple su(2) Lie algebras corresponding to distinct families of scarred eigenstates. Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave product states, |Zn , including ones that show no revivals in the unperturbed PXP model. We discuss the relation between the loose embeddings of Lie algebras present in the PXP model and recent exact constructions of scarred states in related models. arXiv:2001.08232v1 [cond-mat.str-el]

show abstract

“…Recently, there has been a surge in interest of finding and understanding quantum many-body scar states due to the observation of anomalous dynamics in a Rydberg atom experiment [9]. Known systems that host quantum many-body scar states include the PXP model describing the Rydberg-blockaded atom chain [10][11][12][13][14][15][16][17], the Affleck-Kennedy-Lieb-Tasaki model [18][19][20], and the spin-1 XY model [21]. References [22,23] developed a systematic construction to embed nonthermal states in the spectrum.…”

Section: Introductionmentioning

confidence: 99%

Slow thermalization of exact quantum many-body scar states under perturbations

Lin

Chandran

Motrunich

2020

Phys. Rev. Research

View full text Add to dashboard Cite

Quantum many-body scar states are exceptional finite energy density eigenstates in an otherwise thermalizing system that do not satisfy the eigenstate thermalization hypothesis. We investigate the fate of exact many-body scar states under perturbations. At small system sizes, deformed scar states described by perturbation theory survive. However, we argue for their eventual thermalization in the thermodynamic limit from the finite-size scaling of the off-diagonal matrix elements. Nevertheless, we show numerically and analytically that the nonthermal properties of the scars survive for a parametrically long time in quench experiments. We present a rigorous argument that lower bounds the thermalization time for any scar state as t * ∼ O(λ −1/(1+d)), where d is the spatial dimension of the system and λ is the perturbation strength.

show abstract

Connection between quantum-many-body scars and the Affleck–Kennedy–Lieb–Tasaki model from the viewpoint of embedded Hamiltonians

Cited by 85 publications

References 38 publications

Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians

Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians

Quantum scars as embeddings of weakly broken Lie algebra representations

Slow thermalization of exact quantum many-body scar states under perturbations

Contact Info

Product

Resources

About